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Rudder Roll Stabilisation Sea Trials
247
FINAL EXPERIMENTAL RESULTS OF FULL SCALE FINIRUDDER ROLL STABILISATION SEA TRIALS
M.T. Sbarif, G.N. Roberts-, R Sutton-
• Royal Naval Engineering College Manadon, Plymouth, PLS 3A Q, U.K. - Gwent College ofHigher Education, Newport, NP9 SXR. U.K. .- University ofPlymouth, Plymouth, PL4 &AA, U.K.
Abstract. The consequences of roll motions in ship operations can seriously degrade the performance of mechanical and personnel effectiveness. In order to alleviate roll motions many ships are equipped with fin stabilisers. Rudders can also generate roll motions which can be harnessed to function in congress with the fins to accrue enhanced levels of stabilisation. However, in existing ships their contribution to roll stabilisation, without extensive modification to the rudder assembly and power plant, has never been fully realised on account of their limited slew rates. This paper reports on the final phase of full-scale sea trials conducted utilising the existing rudders and fins on board a frigate size warship where various control strategies were employed. Key Words. FinlRudders, Roll Stabilisation, Robust Control
1. INTRODUCTION The pernicious consequences of roll motions have a profound effective on all types of ships. Many devices have been invented and implemented to ameliorate the roll motion. However, few devices have perhaps had the same impact on roll stabilisation as the active fin stabilisation system (Lloyd, 1972). Around the 1950's the Royal Navy formally adopted the resolution to equip all new vessels with these devices as a matter of course. With the advent of the helicopter bearing warships and development of sophisticated weapons systems and radars the decision was judicious. It has been observed in ships, of appropriate size, that when the rudder is 'put-over' the ship initially heels inwards before attaining the steady ' state outward heel angle as it enters the turn (Rawson and Tupper, 1984). Furthermore, this initial roll angle occurs before the ship enters into any yaw motion. Suggesting that the characteristic ephemeral rudder induced roll may be used in congress with the fins to enhance roll stabilisation without significant interference to the heading angles, Rudder Roll Stabilisation (RRS). This potential has been recognised and studies conducted to assess its feasibility (Cowley, 1972).
To date, generally, the implementation of the RRS strategy has been to render the fin stabilisers obsolete, (Amerongen et ai, 1987 and Kallstrom and Schultz, 1990). Since the rudders' slew rate is invariably insufficient, the practice, (Klugt, 1990), is to upgrade the rudder assemblies and associated peripherals. The corollaI)' envisaged, is not that this will accrue greater levels of roll stabilisation than the fins alone, but to eliminate the self generated noise produced by the fins which is detrimental to effective sonar operations, and realise the expected cost benefits. For existing frigates the fins must be retained and to utilise the rudders, without any mechanical modifications. This has provoked the Royal Navy to actively pursue a 'something-for-nothing' technique to utilise both control surfaces despite the limited capability of the rudders in the RRS mode. It affords the advantage that the necessary expenses incurred in improving the rudder servomechanism and assemblies can be avoided. Therefore, there will be three modes of operation~ fins alone, limited stabilisation with rudders alone, and both fins and rudders. In the latter mode, since some stabilisation would be performed by the rudders it will reduce fin activity and hence sonar noise,
248 and en1ulnce the roll amelioration than is possible with either actuating controller engaged alone The aims of the project and this phase of the series of sea-trials are summarised; • To ascertain the feasibility of utilising the rudders in congress with the tins. • Assessment of increase in roll stabilisation with both tins and rudders engaged in stabilisation mode. • Examine the levels of roll stabilisation with tins and rudders engaged individually. with existing controllers and latest robust design techniques. • Assessment of existing tin controllers and RRS augmented autopilot, with the latest control technology. The remainder of this paper is organised as follows: the second section describes the linear mathematical models of ship system and control strategy. Section 3 is a concise overview of the control theory utilised to synthesis the controller and weight selection procedure. Prior to conducting the trials the technical preparations made are briefly outlined. The penultimate section details the trials configurations and the associated results are presented, together with simulation statistics. Finally some inferences are derived with suggested recommendations.
2. SYSTEM MODELLING The ship system is a complex multivariable system but can be simplified if the equations of motion are derived from first principles, separated into lateral and vertical plane motions and assume that no coupling exists between these two classes (Abkowitz, 1972). However, sway, yaw and roll motions have influence on the motions amongst themselves. Such a complex model, which encompasses detailed knowledge of the hydrodynamic parameters and functions in multi-degree-of-freedom mode would be invaluable for simulation and predictions purposes. However, this is type of representation is usually not amenable to control design and a simplified approach is pursued. Each aspect of the system is now considered.
2. J Stabilising Fins The fins act as actuators in the regulation mode; imparting a hydrodynamicaly generated roll moment about the ship's axis of roll, and provided the controller
has been designed correctly, it will oppose the sea induced roll. For control purposes the tin induced roll of the ship must be considered as a single degree of freedom. The following transfer function is derived with the relevant coefficients supplied from sea trials data by (Whalley and Westcott, 1981 and Roberts 1989), and where gI1(s) will be placed in the multivariable context, kll is a speed dependent gain term to encapsulate the increasing moment generating capacity of the tins with ship speed, and Cs is the damping ratio", the roll and 0., fin angles.
41(s) _ 11 _ o.(s) - g (s) -
kll 00; S2
(1)
+ 2l;soo"s + 00;
The tins will not induce any yaw motions on account of their longitudinal centre of roll moment being located very close to the plane of the centre of gravity (CoG). Marshfield (1981) made some tin-induced sway motion measurements on a frigate size warship. He reports insignificant sway generated by the tins. Of course the extent depends on the dihedral angle of the tins (Lloyd, 1989).
2.2 Rudder Dynamics The dynamics of the ship are such that the rudders can be utilised for both course-keeping, which has been well promulgated in literature, and roll stabilisation. In its latter role the rudder employs the peculiar characteristic, that when the rudder is tirst 'put-over' the ship develops a transitory inward heel which appears to be in the wrong sense before attaining the steady-state outward heel. The salient characteristic in this analysis is that minimal yaw motion has occurred. This is indicative of frequency separation between the roll and yaw channels as shown in Figure 1. Therefore, utilising the rudders for roll stabilisation, will not have a detrimental effect on the yaw of the ship Although Blanke and Christensen (1993) and Broome (1979) suggest that this yaw/roll coupling is Significant, real sea trials experience has shown that appropriate filters can be installed as a contingency against this scenario, (Amerongen, et 01 1987). The transfer function which replicates this rudder/roll behaviour is derived from full-scale sea trials (2), where kl2 is analogous to k ll ,
253 , ---------------------~ .. C.C. : ......
..
ccu~-~--
demand values. The last colwnn corresponding values using the PAT91.
shows
the
.
Table 1· Results for sequence one Sea Trials
Model RMS
-
- -------- - -----------~ '
------------------- - --~
Figure 9 : Interconnections scheme
5. RESULTS A large number of individual trials were conducted with various controllers and modes of fin/rudder operation. The fins and rudders were engaged with two different sequences; namely rudders alone and fins with rudder stabilisation. Each sequence was for a duration of 420 seconds. For the entire duration of the trials the sea remained at around state two-three and at predominantly beam seas. Unfortunately, such calm weather is not expedient for roll stabilisation trials and any conclusions derived must be tenuous at best. Typical roll motions which were experienced are shown in Figure 10. The data was subsequently analysed and presented in terms of RMS values and significant heights. It was also decided to conduct a parallel simulations study using the P AT91 sea-keeping software at DRA Haslar.
RoIlRMS
Fin Demand
PAT91
Headq
Rudder Demand
Roll Rudder
Error
Time (I) <120 >120 <120 >120 <120 >120 <120 >120 Dla
Dla
Classic:al
0.7
0.6
8
0
LQG
0.31
0.41
4
1.12
1.61
10.5
0.26
0.18
0.5
3.7
4.24
0.28
0.26 0.33
4.1
6.11
0.27
0.28
1.4
5.8
2.9
2.71
0
3.78
0
4.09
These are the typical values obtained with each type of controller. The fin controller employed in this case was the one currently fitted on board the ship. Before the RRS is implemented the RMS of the rudder is that of the autopilot and thereafter of the two signals summed. The PAT91 roll and rudder demand results are with the RRS permanently engaged. They correlate well with the experimental values. The rudder is relatively less effective in terms of its moment generating capability as compared with the fins, subsequently the marginal increase in RMS roll, in all cases, may be indicative of this feature.
5.2 Fin Stabilisation and RRS Active The primary aim of this project was to ascertain the efficacy of the rudders as secondaly stabilisers. To these ends the next sequence of trials were performed with the fins permanently engaged and controlled by the CCU signals. The rudders were activated for stabilisation after 120 seconds. The results are shown at Table 2 again with the PAT91 predicted RMS values. As expected. since a portion of the stabilisation is performed by the rudders, roll and fin activity both diminish, with the H controller consistently yielding better results. 00
.
Table 2· Results for sequence two
--,
~~-Za~~--~.--~.~-=.--~'a
Figure 10 : Typical roll motions experienced
5.1 Rudder Roll Stabilisation In this sequence of trials the ship was stabilised using the fins for the first 120 seconds. The fins were then switched off and the rudder stabilisation activated. Table 1 shows the typical RMS roll and controller
Model
RRS
Sea Trials
RolIRMS
Fin Demand
PAT91
Rudder Demand
Headq
Roll Rudder
Error
Time (s) <120 >120 <120 >120 <120 >120 <120 >120 Dla
Dla
Classic:al 0.59 0.52
0.44 0.42 0.17
2.59
0.39 0.35
0.6
4.1
0.35
0.8
4.5
LQG H_
7.4
6.3
\.B8
2.5 4.8
0.45 158
5.8
3.3
1.78 0.41 9.92
5.21
1.47 4.69
0.75
0.35
Comparing the trials data with the PAT91 simulations Table 2 shows the predictions to be accurate given th~ relatively small magnitudes of motion. The trials' sea states and pertinent conditions were emulated on PAT91 using a conjectured CCU fin controller which replicates
254
similar levels of stabilisation as demonstrated by the trials data. Again. in the PAT91 simulations, the H_ controllers consistently performed well in changing sea conditions as compared with other controllers. At the outset it was envisaged that the stabilisation of the ship via fins and rudders will be controlled completely from the computer generated demand signals, permitting extensive comparison of various controllers in fin alone stabilisation mode to be performed. Unfortwlately, the sea conditions did not permit this.
6. DISCUSSION and CONCLUSIONS
As mentioned earlier the sea state remained very low through~ut the trials. Such comparatively small amplitudes of motion did not greatly exert the controllers and therefore, their full effectiveness cannot be appreciated. Furthermore, due to ship operations the speed remained at 12-16 knots, limiting the moment generating capabilities of the actuators. Despite these unsuitable environmental conditions valuable conclusions can be derived from the trials data acquired. Sequence 1 manifests the similar effectiveness of the rudders with the fins in roll stabilisation at low sea states. The trials vindicated the most important objective, that of employing the rudders in a supplementary role with the fins enhances roll stabilisation, as can be demonstrated by the results from Sequence 2 and Table 2. The trials results compare favourably with the time simulation data generated at the design stage, affording considerable confidence in the mathematical models for future control design and the numerical integration routines embedded in the simulations software. Comparing the simulations with the real data there is evidence that the robust type controllers yield greater roll amelioration. The PAT91 sea-keeping program verified the sea trials results and the time simulations. They indicate that the potential for using the rudders in concert with the fins as stabilisers is yet to be realised. Again the robust type controller gives the best performance.
7. REFERENCES Abkowitz, M.A. (1972) Stability and Motion Control of Ocean Vehicles. MIT Press Amerongen, l van, P.G.M. van der Klugt, lB.M. Pieffers, (1987) Rudder Roll Stabilisation-
Controller Design and Experimental Results. 8111 Ship Control Systems Symposium, The Hague, Vol. 2 Blanke, M, A.C. Christensen (1993) Rudder-Roll Damping Autopilot Robustness to Sway-raw-Roll Couplings. 10111 SCSS, Ottawa Broome, OR (1979) An Integrated Ship Control System for cs Manchester Challenge. Royal Institute of Naval Architects Cowley, W.E., (1972) The Use of Rudder as Roll Stabiliser 31<1 SCSS, Bath Ooyle, I.C. (1982) Performance and Robustness Analysis for Structured Uncertainty. Proc IEEE Conf. Decision and Control Grimble, M.I., M.R Katebi, Y. Zbang (1993) H_ Based Ship Fin-Rudder Roll Stabilisation Design. 10111 SCSS, Ottawa Vol. 5 KalIstrom, C.G., W.L. Schultz, (1990) An Integrated Control System for Roll Damping and Course Maintenance. 9111 SCSS, Bethesda, Vol. 3 Klugt, P.G.M. van der, (1990) ASSA: The RRS Autopilot for Dutch M-Class. 9 th SCSS, Bethesda, Vol. 2 L1oyd, A.RlM. (1972) HydrodynamiC Peiformance of Roll Stabiliser Fins. 31<1 SCSS, Bath L1oyd, A.RI.M. (1989) Sea-keeping: Ship Behaviour in Rough Weather. Ellis Horwood Maceijowski, I.M. (1989) Multivariable Feedback Design. Addison-Wesley Marshfield, W.B. (1981) HMS •••••• Roll Stabiliser Trials ORA Haslar Report No. AMTE(H), R81012, Restricted Rawson, K.l, E.C. Tupper, (1984) Basic Ship Theory. Longman Roberts, G.N. (1989) Ship Motion Control Using a Multivarible Approach. PhD Thesis, University of Wales Sharif, MT., G.N. Roberts, R Sunon Full-Scale Experimental Results of FinlRudder Roll Stabilisation, MCMC'94, Southampton Whalley, R, 1. W. Westcon (1981) Ship Motion Control. 6th SCSS, The Hague, Vol. H
8. ACKNOWLEDGEMENTS The authors wish to express their gratitude to the MoD (ES251) for tlleir continual support and encouragement on this project. The facilities made available and advise given by ORA Haslar, and in particular from Paul Crossland, were greatly appreciated.
FINAL EXPERIMENTAL RESULTS OF FULL SCALE FINIRUDDER ROLL STABILISATION SEA TRIALS
M.T. Sbarif, G.N. Roberts-, R Sutton-
• Royal Naval Engineering College Manadon, Plymouth, PLS 3A Q, U.K. - Gwent College ofHigher Education, Newport, NP9 SXR. U.K. .- University ofPlymouth, Plymouth, PL4 &AA, U.K.
Abstract. The consequences of roll motions in ship operations can seriously degrade the performance of mechanical and personnel effectiveness. In order to alleviate roll motions many ships are equipped with fin stabilisers. Rudders can also generate roll motions which can be harnessed to function in congress with the fins to accrue enhanced levels of stabilisation. However, in existing ships their contribution to roll stabilisation, without extensive modification to the rudder assembly and power plant, has never been fully realised on account of their limited slew rates. This paper reports on the final phase of full-scale sea trials conducted utilising the existing rudders and fins on board a frigate size warship where various control strategies were employed. Key Words. FinlRudders, Roll Stabilisation, Robust Control
1. INTRODUCTION The pernicious consequences of roll motions have a profound effective on all types of ships. Many devices have been invented and implemented to ameliorate the roll motion. However, few devices have perhaps had the same impact on roll stabilisation as the active fin stabilisation system (Lloyd, 1972). Around the 1950's the Royal Navy formally adopted the resolution to equip all new vessels with these devices as a matter of course. With the advent of the helicopter bearing warships and development of sophisticated weapons systems and radars the decision was judicious. It has been observed in ships, of appropriate size, that when the rudder is 'put-over' the ship initially heels inwards before attaining the steady ' state outward heel angle as it enters the turn (Rawson and Tupper, 1984). Furthermore, this initial roll angle occurs before the ship enters into any yaw motion. Suggesting that the characteristic ephemeral rudder induced roll may be used in congress with the fins to enhance roll stabilisation without significant interference to the heading angles, Rudder Roll Stabilisation (RRS). This potential has been recognised and studies conducted to assess its feasibility (Cowley, 1972).
To date, generally, the implementation of the RRS strategy has been to render the fin stabilisers obsolete, (Amerongen et ai, 1987 and Kallstrom and Schultz, 1990). Since the rudders' slew rate is invariably insufficient, the practice, (Klugt, 1990), is to upgrade the rudder assemblies and associated peripherals. The corollaI)' envisaged, is not that this will accrue greater levels of roll stabilisation than the fins alone, but to eliminate the self generated noise produced by the fins which is detrimental to effective sonar operations, and realise the expected cost benefits. For existing frigates the fins must be retained and to utilise the rudders, without any mechanical modifications. This has provoked the Royal Navy to actively pursue a 'something-for-nothing' technique to utilise both control surfaces despite the limited capability of the rudders in the RRS mode. It affords the advantage that the necessary expenses incurred in improving the rudder servomechanism and assemblies can be avoided. Therefore, there will be three modes of operation~ fins alone, limited stabilisation with rudders alone, and both fins and rudders. In the latter mode, since some stabilisation would be performed by the rudders it will reduce fin activity and hence sonar noise,
248 and en1ulnce the roll amelioration than is possible with either actuating controller engaged alone The aims of the project and this phase of the series of sea-trials are summarised; • To ascertain the feasibility of utilising the rudders in congress with the tins. • Assessment of increase in roll stabilisation with both tins and rudders engaged in stabilisation mode. • Examine the levels of roll stabilisation with tins and rudders engaged individually. with existing controllers and latest robust design techniques. • Assessment of existing tin controllers and RRS augmented autopilot, with the latest control technology. The remainder of this paper is organised as follows: the second section describes the linear mathematical models of ship system and control strategy. Section 3 is a concise overview of the control theory utilised to synthesis the controller and weight selection procedure. Prior to conducting the trials the technical preparations made are briefly outlined. The penultimate section details the trials configurations and the associated results are presented, together with simulation statistics. Finally some inferences are derived with suggested recommendations.
2. SYSTEM MODELLING The ship system is a complex multivariable system but can be simplified if the equations of motion are derived from first principles, separated into lateral and vertical plane motions and assume that no coupling exists between these two classes (Abkowitz, 1972). However, sway, yaw and roll motions have influence on the motions amongst themselves. Such a complex model, which encompasses detailed knowledge of the hydrodynamic parameters and functions in multi-degree-of-freedom mode would be invaluable for simulation and predictions purposes. However, this is type of representation is usually not amenable to control design and a simplified approach is pursued. Each aspect of the system is now considered.
2. J Stabilising Fins The fins act as actuators in the regulation mode; imparting a hydrodynamicaly generated roll moment about the ship's axis of roll, and provided the controller
has been designed correctly, it will oppose the sea induced roll. For control purposes the tin induced roll of the ship must be considered as a single degree of freedom. The following transfer function is derived with the relevant coefficients supplied from sea trials data by (Whalley and Westcott, 1981 and Roberts 1989), and where gI1(s) will be placed in the multivariable context, kll is a speed dependent gain term to encapsulate the increasing moment generating capacity of the tins with ship speed, and Cs is the damping ratio", the roll and 0., fin angles.
41(s) _ 11 _ o.(s) - g (s) -
kll 00; S2
(1)
+ 2l;soo"s + 00;
The tins will not induce any yaw motions on account of their longitudinal centre of roll moment being located very close to the plane of the centre of gravity (CoG). Marshfield (1981) made some tin-induced sway motion measurements on a frigate size warship. He reports insignificant sway generated by the tins. Of course the extent depends on the dihedral angle of the tins (Lloyd, 1989).
2.2 Rudder Dynamics The dynamics of the ship are such that the rudders can be utilised for both course-keeping, which has been well promulgated in literature, and roll stabilisation. In its latter role the rudder employs the peculiar characteristic, that when the rudder is tirst 'put-over' the ship develops a transitory inward heel which appears to be in the wrong sense before attaining the steady-state outward heel. The salient characteristic in this analysis is that minimal yaw motion has occurred. This is indicative of frequency separation between the roll and yaw channels as shown in Figure 1. Therefore, utilising the rudders for roll stabilisation, will not have a detrimental effect on the yaw of the ship Although Blanke and Christensen (1993) and Broome (1979) suggest that this yaw/roll coupling is Significant, real sea trials experience has shown that appropriate filters can be installed as a contingency against this scenario, (Amerongen, et 01 1987). The transfer function which replicates this rudder/roll behaviour is derived from full-scale sea trials (2), where kl2 is analogous to k ll ,
253 , ---------------------~ .. C.C. : ......
..
ccu~-~--
demand values. The last colwnn corresponding values using the PAT91.
shows
the
.
Table 1· Results for sequence one Sea Trials
Model RMS
-
- -------- - -----------~ '
------------------- - --~
Figure 9 : Interconnections scheme
5. RESULTS A large number of individual trials were conducted with various controllers and modes of fin/rudder operation. The fins and rudders were engaged with two different sequences; namely rudders alone and fins with rudder stabilisation. Each sequence was for a duration of 420 seconds. For the entire duration of the trials the sea remained at around state two-three and at predominantly beam seas. Unfortunately, such calm weather is not expedient for roll stabilisation trials and any conclusions derived must be tenuous at best. Typical roll motions which were experienced are shown in Figure 10. The data was subsequently analysed and presented in terms of RMS values and significant heights. It was also decided to conduct a parallel simulations study using the P AT91 sea-keeping software at DRA Haslar.
RoIlRMS
Fin Demand
PAT91
Headq
Rudder Demand
Roll Rudder
Error
Time (I) <120 >120 <120 >120 <120 >120 <120 >120 Dla
Dla
Classic:al
0.7
0.6
8
0
LQG
0.31
0.41
4
1.12
1.61
10.5
0.26
0.18
0.5
3.7
4.24
0.28
0.26 0.33
4.1
6.11
0.27
0.28
1.4
5.8
2.9
2.71
0
3.78
0
4.09
These are the typical values obtained with each type of controller. The fin controller employed in this case was the one currently fitted on board the ship. Before the RRS is implemented the RMS of the rudder is that of the autopilot and thereafter of the two signals summed. The PAT91 roll and rudder demand results are with the RRS permanently engaged. They correlate well with the experimental values. The rudder is relatively less effective in terms of its moment generating capability as compared with the fins, subsequently the marginal increase in RMS roll, in all cases, may be indicative of this feature.
5.2 Fin Stabilisation and RRS Active The primary aim of this project was to ascertain the efficacy of the rudders as secondaly stabilisers. To these ends the next sequence of trials were performed with the fins permanently engaged and controlled by the CCU signals. The rudders were activated for stabilisation after 120 seconds. The results are shown at Table 2 again with the PAT91 predicted RMS values. As expected. since a portion of the stabilisation is performed by the rudders, roll and fin activity both diminish, with the H controller consistently yielding better results. 00
.
Table 2· Results for sequence two
--,
~~-Za~~--~.--~.~-=.--~'a
Figure 10 : Typical roll motions experienced
5.1 Rudder Roll Stabilisation In this sequence of trials the ship was stabilised using the fins for the first 120 seconds. The fins were then switched off and the rudder stabilisation activated. Table 1 shows the typical RMS roll and controller
Model
RRS
Sea Trials
RolIRMS
Fin Demand
PAT91
Rudder Demand
Headq
Roll Rudder
Error
Time (s) <120 >120 <120 >120 <120 >120 <120 >120 Dla
Dla
Classic:al 0.59 0.52
0.44 0.42 0.17
2.59
0.39 0.35
0.6
4.1
0.35
0.8
4.5
LQG H_
7.4
6.3
\.B8
2.5 4.8
0.45 158
5.8
3.3
1.78 0.41 9.92
5.21
1.47 4.69
0.75
0.35
Comparing the trials data with the PAT91 simulations Table 2 shows the predictions to be accurate given th~ relatively small magnitudes of motion. The trials' sea states and pertinent conditions were emulated on PAT91 using a conjectured CCU fin controller which replicates
254
similar levels of stabilisation as demonstrated by the trials data. Again. in the PAT91 simulations, the H_ controllers consistently performed well in changing sea conditions as compared with other controllers. At the outset it was envisaged that the stabilisation of the ship via fins and rudders will be controlled completely from the computer generated demand signals, permitting extensive comparison of various controllers in fin alone stabilisation mode to be performed. Unfortwlately, the sea conditions did not permit this.
6. DISCUSSION and CONCLUSIONS
As mentioned earlier the sea state remained very low through~ut the trials. Such comparatively small amplitudes of motion did not greatly exert the controllers and therefore, their full effectiveness cannot be appreciated. Furthermore, due to ship operations the speed remained at 12-16 knots, limiting the moment generating capabilities of the actuators. Despite these unsuitable environmental conditions valuable conclusions can be derived from the trials data acquired. Sequence 1 manifests the similar effectiveness of the rudders with the fins in roll stabilisation at low sea states. The trials vindicated the most important objective, that of employing the rudders in a supplementary role with the fins enhances roll stabilisation, as can be demonstrated by the results from Sequence 2 and Table 2. The trials results compare favourably with the time simulation data generated at the design stage, affording considerable confidence in the mathematical models for future control design and the numerical integration routines embedded in the simulations software. Comparing the simulations with the real data there is evidence that the robust type controllers yield greater roll amelioration. The PAT91 sea-keeping program verified the sea trials results and the time simulations. They indicate that the potential for using the rudders in concert with the fins as stabilisers is yet to be realised. Again the robust type controller gives the best performance.
7. REFERENCES Abkowitz, M.A. (1972) Stability and Motion Control of Ocean Vehicles. MIT Press Amerongen, l van, P.G.M. van der Klugt, lB.M. Pieffers, (1987) Rudder Roll Stabilisation-
Controller Design and Experimental Results. 8111 Ship Control Systems Symposium, The Hague, Vol. 2 Blanke, M, A.C. Christensen (1993) Rudder-Roll Damping Autopilot Robustness to Sway-raw-Roll Couplings. 10111 SCSS, Ottawa Broome, OR (1979) An Integrated Ship Control System for cs Manchester Challenge. Royal Institute of Naval Architects Cowley, W.E., (1972) The Use of Rudder as Roll Stabiliser 31<1 SCSS, Bath Ooyle, I.C. (1982) Performance and Robustness Analysis for Structured Uncertainty. Proc IEEE Conf. Decision and Control Grimble, M.I., M.R Katebi, Y. Zbang (1993) H_ Based Ship Fin-Rudder Roll Stabilisation Design. 10111 SCSS, Ottawa Vol. 5 KalIstrom, C.G., W.L. Schultz, (1990) An Integrated Control System for Roll Damping and Course Maintenance. 9111 SCSS, Bethesda, Vol. 3 Klugt, P.G.M. van der, (1990) ASSA: The RRS Autopilot for Dutch M-Class. 9 th SCSS, Bethesda, Vol. 2 L1oyd, A.RlM. (1972) HydrodynamiC Peiformance of Roll Stabiliser Fins. 31<1 SCSS, Bath L1oyd, A.RI.M. (1989) Sea-keeping: Ship Behaviour in Rough Weather. Ellis Horwood Maceijowski, I.M. (1989) Multivariable Feedback Design. Addison-Wesley Marshfield, W.B. (1981) HMS •••••• Roll Stabiliser Trials ORA Haslar Report No. AMTE(H), R81012, Restricted Rawson, K.l, E.C. Tupper, (1984) Basic Ship Theory. Longman Roberts, G.N. (1989) Ship Motion Control Using a Multivarible Approach. PhD Thesis, University of Wales Sharif, MT., G.N. Roberts, R Sunon Full-Scale Experimental Results of FinlRudder Roll Stabilisation, MCMC'94, Southampton Whalley, R, 1. W. Westcon (1981) Ship Motion Control. 6th SCSS, The Hague, Vol. H
8. ACKNOWLEDGEMENTS The authors wish to express their gratitude to the MoD (ES251) for tlleir continual support and encouragement on this project. The facilities made available and advise given by ORA Haslar, and in particular from Paul Crossland, were greatly appreciated.